Abstract
Lucio Mare and Roger Ariew (University of South Florida, USA) in The Individual in Leibniz’s Philosophy, 1663–1686 show that the notions of being and unity are mutually supporting; as Leibniz said to Arnauld “I hold this identical proposition, differentiated only by the emphasis, to be an axiom, namely, that what is not truly one being is not truly one being either.” The authors shed light on Leibniz’s changing notions of substance and being by concentrating on his changing views about unity and the individual, from his early Bachelor’s thesis (Disputatio Metaphysica de Principio Individui, 1663), to his middle period treatise Discours de Métaphysique (1686). In the process, the authors also discuss Leibniz’s views about individuation in De Transubstantiatione (1668), Confessio Philosophi (1672–1673?), Meditatio de Principio Individui (1676), some of his correspondence with Jakob Thomasius (1668–1669), Notationes generales (1683–1685?) and his Notes on Cordemoy (Ex Cordemoii Tractatu de Corporis et Mentis Distinctione, 1685), among others. Along the way, the authors discuss the relation of Leibniz’s views with those of others, especially seventeenth-century Scholastics.
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- 1.
It would be unusual, of course, if Leibniz could change his views on matters of physical science and remain constant on the fundamental points of his philosophy. And, in fact, if Garber is right about Leibniz’s changes with respect to body and substance, one would also expect changes with respect to individuation. Following Aristotle, most medieval philosophers commonly endorsed the principle that unity does not add anything to being (Aristotle 1910–1952, Metaphysics, book Γ, 1003b 30–32). In this Aristotelian framework, the axiom refers to the convertibility of unity and being, unity (or oneness) as a transcendental property of being. The notions of being and unity are thus mutually supporting. Leibniz echoes this; as he says to Arnauld, “I hold this identical proposition, differentiated only by the emphasis, to be an axiom, namely, that what is not truly one being is not truly one being either” (30 April 1687, GP II, 97; AG 86). Oneness in this famous Leibnizian aphorism on the convertibility of being and unity has to be understood as pointing at the same time to the indivisibility of the being (by excluding any composition through the addition of parts) and to the uniqueness of that which is the only being that is what it is.
- 2.
See Thomas Aquinas (1964–1976), Summa Theologiae, I, q. 50, art. 4.
- 3.
The mature Leibniz will not be as positive about these Scholastic remnants. Putting a negative twist on the “notable paradox” that two things cannot be perfectly similar, the mature Leibniz will say: “The vulgar philosophers were mistaken when they believed that there are two things different in number alone, or only because they are two, and from this error have arisen their perplexities about what they called the principle of individuation” (GP VII, 395; AG 334). One can see this as Leibniz’s answer to the issue of individuation in his confrontation with Locke and the revival of the problematic of individuality and singularity in the New Essays. Leibniz echoes a passage in which the principle of individuation is said to be something of concern merely in the schools, “where they torment themselves so much in seeking to understand what it is.” In his response he asserts: “The principle of individuation for individuals reduces to the principle of distinction. […] If two individuals were perfectly similar and equal and (in a word) indistinguishable in themselves, there would be no principle of individuation” (GP V, 214).
- 4.
Leibniz argues, in Notationes Generales (Summer 1683–1685?), that singular things are ultimate species, that there can never be two singular things similar in every respect, and that the principle of individuation is always a specific difference; he adds that this is what Saint Thomas said of intelligences, but applied to all individuals. Leibniz considers the example of two eggs and asserts that one should be able to say of one egg something that cannot be said of the other; otherwise, they could be substituted for each other and there would be no reason not to say that we are dealing with one and the same thing. “Hinc porro sequitur Singularia esse revera species infimas, neque umquam dari posse duo singularia per omnia similia et proinde principium individuationis semper esse differentiam aliquam Specificam, quod S. Thomas ajebat de intelligentiis, sed idem est verum de individuis quibuscunque [. . .] exempli causa duo ova, necesse est enim aliqua de uno dici posse quæ de altero dici non possint, alioqui substitui sibi mutuo possint, nec ratio erit cur ita non potius dicantur esse unum et idem” (A VI, 4A, 553).
- 5.
Scipion Dupleix (1992), La Metaphysique, 233.
- 6.
Dupleix (1992), La Metaphysique, 235.
- 7.
Dupleix (1992), La Metaphysique, 232.
- 8.
René de Ceriziers similarly refers to two groups: (1) those who accept “a real difference that determines the thing’s particular nature, in the way Rational restricts animal to the species of man,” presumably the Scotists, and (2) those who “think that the principle of individuation is nothing more than the concourse and multitude of the accidents that befall the substantial being of the individual” (De Ceriziers 1643, Le Philosophe Français 3, 31). De Ceriziers rejects both of these principles of individuation. Théophraste Bouju also gives a similar argument, but from a Thomist perspective, against those who hold that something is singular by its essence and by its accidents all together, which, he claims, would be not different from the Scotist view that the thing is individuated by its essence alone. Bouju asserts: “The singularity of the thing would be distinguished only rationally from the whole thing, which would amount to things being neither universal nor singular by themselves, but through the consideration of the understanding” (Bouju 1614, Corps de toute la philosophie, 237).
- 9.
The full title is Disputatio Metaphysica/De/Principio Individvi,/Quam/Deo O. M. Annuente/Et/Indultu Inclytæ Philosoph. Facultatis/In Illustri Academiâ Lipsiensi/Præside/Viro Excellentissimo et Clarissimo/Dn. M. Jacobo Thomasio/Eloqvent. P. P. Min. Princ. Colleg./Collegiato/Præceptore et Fautore suo Maximo/Publicè ventilandam proponit/Gottfredus Guilielmus/Leibnuzius,/Lips. Philos. et B. A. Baccal./Aut. et Resp./30. Maji Anni MDCLXIII. As one can see, Thomasius is given “top billing” (in the largest font); Leibniz’s name comes in second (and in smaller font). For more on the relations between Thomasius and Leibniz, see Mercer (2002).
- 10.
A VI, 1, 6. This judgment on Greek thought is taken up again in Jakob Thomasius (1665).
- 11.
A VI, 1, 6 and note.
- 12.
Thomasius is representative of a powerful revival of Aristotelianism on the side of Reformation. His polemic against the Scholastics and the Scotists, in particular, is constant; he regards contemporary metaphysical systems such as Clemens Timpler’s or Suárez’ to be ontologically deviant in their lack of theological premises. For more on his judgment of Scotism, see Thomasius (1665).
- 13.
It is generally recognized today that Leibniz constantly endorsed or adhered to a nominalist ontology or epistemology. See Fichant (1998, 147), but also Mugnai (1990). The passage in the correspondence with Arnauld is also a statement of one of the main tenets which make up Leibniz’s “provisional nominalism”: the specific claim to a particularist ontology that only individual substances exist. In a text from 1688 entitled De realitate accidentium, Leibniz defines himself as a nominalist, at least “per provisionem”, see Grua II, 547.
- 14.
Leroy Loemker realized this; in a footnote to the passage he writes: “Leibniz’s departures from Thomism are significant; his view of individuality and of the soul here is Scotistic, though he had earlier rejected Scotus’ principle of individuality. The unity of matter as an aggregate is never itself material but logical and mental. The soul itself, in turn, has its own matter, distinct from its body” (L 120). Loemker is right in thinking of the view as a kind of Scotism, even though, of course, it says nothing about individuals as common nature plus haecceity, two things asserted to be formally distinct. Substantial form as principle of individuation would have been considered by Leibniz in the category of “something less” than whole entity, with a metaphysical part being added to the essence.
- 15.
In 1668, Leibniz adds a Neo-Platonic spin to his conception of substantial forms: substantial forms are ideas in the mind of God.
- 16.
This does not seem very different from Leibniz’s earlier adherence to nominalism in the earlier Disputatio. Yet, explaining the reasons for Leibniz’s rejection of substantial forms in 1668–1670 enables an understanding of the larger context which ultimately led him to positing an external principle of individuation in the Confessio philosophi of 1672.
- 17.
“Demonstratio ex eo principio, quod in corporibus nulla sit origo motus” (A VI, 1, 494).
- 18.
Confessio naturae contra atheistas, GP IV, 108–109: “[…] cum corpora motum habeant, non singula ente incorporali, sed a se invicem.”
- 19.
The prime mover causes the movement of other things as a final cause and not as an efficient cause: it is the purpose, the end of the moving. For Aristotle, an efficient cause imprinting motion onto the world would itself be affected by that movement or push, which it cannot since it is an unmoving cause, Aristotle (1910–1952), Metaphysics, book Λ, 1072 a26–b4.
- 20.
It is worth noting that Leibniz chose to publish the text of this 1669 more extended letter as an Appendix to his own Dissertatio preliminaries to Marius Nizolius’ De veris principiis et vera philosophandi (republished in 1670).
- 21.
The “eduction” of forms from the passive power of matter was a theory held by the majority of medieval philosophers, Aquinas in particular, but also sixteenth century textbook authors, such as Franciscus Toletus and Benito Pereira.
- 22.
A II, 1, 22: “Ita reditur ad tot deunculos, quot formas substantiales […].”
- 23.
Divine ideas are the substance of things: “Ideae Dei et Substantiae rerum sunt idem re […]” (A VI, 1, 513).
- 24.
That is, according to the Aristotelian-Thomistic dictum. “Nam Ens per se subsistens seu substantia hæc vel illa in individuo sumta est Suppositum. (Scholastici enim in usu habent Suppositum definire individuum Substantiale). Iam actiones sunt Suppositorum” (A VI, 1, 497).
- 25.
The conspectus of Catholic Demonstrations included, in its 3rd part, a chapter on the Augustinian congruentia incarnationis and a reference to Saint Anselm’s Cur Deus homo. The next chapter, on incarnation, was planned: “contra Arianos et Nestorianos” (A VI, 1, 497).
- 26.
Scholia, A VI, 1, 510.
- 27.
Catéchisme du Concile de Trente, Marbeau-Charpentier (1923), II, XIX, 1.
- 28.
In the first fragment on the Eucharist from 1668, Leibniz had specifically criticized Thomas White’s analogy between transubstantiation and augmentatio: A VI, 1, 501.
- 29.
Porphyry (1998, 15), Isagoge, V, 1.
- 30.
Aristotle also exposes this principle in the 10th book of his Categories. For a detailed analysis of the use of this principle as a weapon against atomism, see Newman (2006, 50–54; 104–105; 115–116).
- 31.
Aristotle (1910–1952), Categories, X, 13 a 17.
- 32.
Even though his reflection on the Elementa de Mente and de Corpore continues to develop (as announced in the 1668–1669 plan of the Catholic Demonstrations – A II, 1, 175–176). This also raises doubts whether anything like a primitive theory of complete concepts is developed at an early stage in Leibniz’s thought.
- 33.
Sleigh (2005, 104–105). The paragraph continues: “For no man reasons otherwise when he must distinguish things that are entirely similar.” Leibniz’s distancing himself from the Scholastics in the Confessio takes on greater import when one considers his deep knowledge of Scholasticism, knowledge he himself is proud of. In a 1678 letter to Herman Conring, Leibniz felt he needed to defend himself against the accusation that he simply did not know any Scholastic philosophy: “You say that my estimate of the Schoolmen’s metaphysics would be more favorable if I had read them.” Leibniz responded: “Yet I esteemed [the Schoolmen’s metaphysics] most favorably, for I had written to you, if you remember well, that I believe many excellent metaphysical demonstrations are to be found in them which deserve to be purged of their barbarism and confusion. And I could not have said this if I had not wanted you to believe that I had read them.” Leibniz claimed that he had examined the writings of the Scholastics, and done so even “more immoderately and eagerly” than his teachers approved, so that they “feared that he would cling too tightly to these rocks.” He also claimed that when he began to study philosophy at the universities he made “some original and profound comments” on Scholastic topics, such as “the principle of individuation,” and he “never since regretted having sampled these studies” (GP I, 197–98; L 190).
- 34.
A, II 1, 16: Leibniz introduces the 13th c. medieval distinction between the form of the whole and the form of the part, while considering haecceity to be “more like form since it contracts and distinguishes.”
- 35.
Confessio philosophi, A VI, 3, 147.
- 36.
The concept of haecceity will further evolve up until the period of the Discourse on metaphysics and afterwards, when Leibniz would define individuals as haecceities: “where there is space and time.” De divisione praedicati: “Individualia seu haecceitates ubi locus et tempus” (A VI, 4A, 927). Thus Leibniz reinstates the Scotistic principle of haecceitas in an un-Scotisfic fashion, as quantity, understanding the latter in a vaguely realistic sense, as the true “principle of individuation” for physical beings. He states, as definitions in another 1672 essay: “Quantitas est modus, quo res cogitator determinate, aut potius quo res cogitator tota. […] Seu quantitas est ipsa haecceitas, qua res cogitator haec. Qualitas est modus, quo res cogitator mutabilis seu posse agree et pati. Quo res cogitator cum relatione non ad sensum, sed intellectum. Quantitatis enim est conceptio relationis rei ad sensum. Hinc ratio patet cur sola ex accidentibus quantitas auferri non possit, continet enim ipsam rei haecceitatem” (A VI, 2, 488–489). This kind of conflation between haecceity and quantity, or haecceity as the spatio-temporal circumstances which individuate a substance (in the Confessio philosophi, 1672–1673) brings to mind the Neo-Platonic residues in the final corollaries of the Disputatio, where Leibniz considers that the essences of things are like numbers or that matter possesses its own actus entitativus and is realiter identical with quantity. It might be interesting to see, in this regard, what influence Erhard Weigel, Leibniz’s other philosophy teacher, might have had on him; see Piro (2005, 10).
- 37.
We can now reaffirm the inference that Leibniz did not hold the complete concept view of substance and the identity of indiscernibles in 1663.
- 38.
Leibniz’s critique of extension is yet again concerned with temporality. Extension is not a constituent element of things, but the diffusion, extending of one thing. Leibniz believes there is a central difficulty in Descartes in conceiving the relationship between substance (to which extension is an attribute) and duration (which is but a mode). Extension cannot account for substance since it is temporally bound to the present and merely sequential: it reflects only a precise moment in the successive state of things, as a sequence in the development of phenomena. Therefore it cannot account for all present and future states or developments of a substance. This is where the need for the internalization of spatio-temporal individuating accidents (Confessio philosophi) and something of a mind-like nature, endowed with memory and a history, intervenes. This temporal aspect of substances will be later fulfilled by the concept of force: derivative force both is and expresses the present state of a substance. Force expresses the present state of a substance by being the link between its past states and its future ones.
- 39.
A VI, 3, 491; also Parkinson (1992, 51–53).
- 40.
Leibniz, A VI, 3, 491; Parkinson (1992, 51). The argument is repeated as late as 1685 in Leibniz’s “Notes on Cordemoy’s Treatise On the Distinction between Body and Mind,” as a criticism of Cordemoy’s atomist solution to the Cartesian problem of individuation; although he appreciated Cordemoy’s criticism of Cartesianism, Leibniz thought Cordemoy had not gone far enough with his solution. As Leibniz said, “These are difficulties for Cordemoy himself: let us suppose two triangular atoms come into contact and compose a perfect square, and that they rest next to each other in this way, and let there be another corporeal substance or atom, a square one equal to the other two. I ask, in what respect do these two extended things differ? Certainly no difference can be conceived in them as they are now, unless we suppose something in bodies besides extension; rather they are distinguished solely by memory of their former condition and there is nothing of this kind in bodies” (A VI, 4, 1799; Arthur 279). The example of the two triangles, reconsidered in three dimensions, continues to play a role in Leibniz’s thinking even in the 1690s, in an argument against atoms separate from the issue of individuation (see GP VII, 284–85).
- 41.
See, in particular, his Notes on Science and Metaphysics (18 March 1676, Arthur 55).
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Mare, L., Ariew, R. (2015). The Individual in Leibniz’s Philosophy, 1663–1686. In: Nita, A. (eds) Leibniz’s Metaphysics and Adoption of Substantial Forms. The New Synthese Historical Library, vol 74. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9956-0_2
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